Artifacts by baking texture (diffuse)
The jagged lines in the bake could be caused by a few different things:


Texture Filtering
Bad UV Map
Small Texture Size


1) Cycles image textures have an option in the node for Linear, Closest, or Cubic filtering (Smart is an option if you're using OSL). Try setting this to Cubic.
2)Even if you have a large image, it may be that the UV map in this region is too small to make effective use of the image space. Try altering your UV map to fill more of the image area, if you can.
3) You might just have a really small texture size, so the lines are jagged at that point. I can see the pixels, so this is probably it. Try baking at a higher resolution

Finally, you might use KRITA or GIMP to add a Gaussian blur to the image. You could also use Blender's compositor to do this.